相关论文: A High Order Multi-Dimensional Characteristic Trac…

We present a novel method for solving the linearized Vlasov--Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution…

Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…

We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift-diffusion-Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the…

High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…

We propose a high-order numerical methodology for computing the ground state and time evolution of the two-dimensional Gross-Pitaevskii equation with harmonic trapping potential. The ground state is obtained by combining normalized gradient…

In this letter, we provide counter-examples to demonstrate that it is possible to retain second-order accuracy using Sakurai et al.'s method, even when different flux boundary conditions are imposed on multiple interfaces that do not…

The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchm\"{u}ller and Helzel can retain the full order of accuracy of the one-dimensional WENO reconstruction and requires only one flux…

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…

We propose an algorithm for solution of high-dimensional evolutionary equations (ODEs and discretized time-dependent PDEs) in the Tensor Train (TT) decomposition, assuming that the solution and the right-hand side of the ODE admit such a…

Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…

Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the…

This work presents a multigrid preconditioned high order immersed finite difference solver to accurately and efficiently solve the Poisson equation on complex 2D and 3D domains. The solver employs a low order Shortley-Weller multigrid…

We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…

Visual tracking is typically solved as a discriminative learning problem that usually requires high-quality samples for online model adaptation. It is a critical and challenging problem to evaluate the training samples collected from…

Certain features of the method of characteristics are of considerable interest in relation with Vlasov simulation [H. Abbasi {\it et al}, Phys. Rev. E \textbf{84}, 036702 (2011)]. A Vlasov simulation scheme of this kind can be recurrence…

In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our…

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the…

This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a $d$-dimensional hypercube. Our scheme produces a symmetric linear system: an important property that does not…

This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…

Tensor decomposition, a collection of factorization techniques for multidimensional arrays, are among the most general and powerful tools for scientific analysis. However, because of their increasing size, today's data sets require more…